Properties

Label 2576.2.a.bb.1.2
Level $2576$
Weight $2$
Character 2576.1
Self dual yes
Analytic conductor $20.569$
Analytic rank $0$
Dimension $5$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 2576 = 2^{4} \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 2576.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(20.5694635607\)
Analytic rank: \(0\)
Dimension: \(5\)
Coefficient field: 5.5.6963152.1
Defining polynomial: \( x^{5} - 2x^{4} - 10x^{3} + 10x^{2} + 29x + 10 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 644)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.2
Root \(-1.18229\) of defining polynomial
Character \(\chi\) \(=\) 2576.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.18229 q^{3} +4.04332 q^{5} +1.00000 q^{7} +1.76237 q^{9} +O(q^{10})\) \(q-2.18229 q^{3} +4.04332 q^{5} +1.00000 q^{7} +1.76237 q^{9} +3.98384 q^{11} +6.74621 q^{13} -8.82367 q^{15} -4.92849 q^{17} +1.24680 q^{19} -2.18229 q^{21} +1.00000 q^{23} +11.3484 q^{25} +2.70086 q^{27} +6.48443 q^{29} +8.38256 q^{31} -8.69387 q^{33} +4.04332 q^{35} -7.61137 q^{37} -14.7222 q^{39} -7.11078 q^{41} +1.11777 q^{43} +7.12582 q^{45} -8.31426 q^{47} +1.00000 q^{49} +10.7554 q^{51} -4.77154 q^{53} +16.1079 q^{55} -2.72088 q^{57} -1.31712 q^{59} +0.838914 q^{61} +1.76237 q^{63} +27.2771 q^{65} -12.4350 q^{67} -2.18229 q^{69} -10.0613 q^{71} +6.46827 q^{73} -24.7655 q^{75} +3.98384 q^{77} +6.45910 q^{79} -11.1812 q^{81} +5.59303 q^{83} -19.9275 q^{85} -14.1509 q^{87} -10.2619 q^{89} +6.74621 q^{91} -18.2931 q^{93} +5.04121 q^{95} +11.2477 q^{97} +7.02099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 5 q - 3 q^{3} + 2 q^{5} + 5 q^{7} + 10 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 5 q - 3 q^{3} + 2 q^{5} + 5 q^{7} + 10 q^{9} - 2 q^{11} + 13 q^{13} - 4 q^{15} + 4 q^{17} - 12 q^{19} - 3 q^{21} + 5 q^{23} + 19 q^{25} - 15 q^{27} + 13 q^{29} + 3 q^{31} + 24 q^{33} + 2 q^{35} - 4 q^{37} - 3 q^{39} + q^{41} + 8 q^{43} - 16 q^{45} - 5 q^{47} + 5 q^{49} + 16 q^{51} - 8 q^{53} + 2 q^{55} + 12 q^{57} - 12 q^{59} + 20 q^{61} + 10 q^{63} - 12 q^{65} + 12 q^{67} - 3 q^{69} - 9 q^{71} - 9 q^{73} - 35 q^{75} - 2 q^{77} + 8 q^{79} - 11 q^{81} + 28 q^{83} + 16 q^{85} + 15 q^{87} + 32 q^{89} + 13 q^{91} - 15 q^{93} + 36 q^{95} + 4 q^{97} - 28 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.18229 −1.25994 −0.629972 0.776618i \(-0.716933\pi\)
−0.629972 + 0.776618i \(0.716933\pi\)
\(4\) 0 0
\(5\) 4.04332 1.80823 0.904113 0.427293i \(-0.140533\pi\)
0.904113 + 0.427293i \(0.140533\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) 1.76237 0.587456
\(10\) 0 0
\(11\) 3.98384 1.20117 0.600586 0.799560i \(-0.294934\pi\)
0.600586 + 0.799560i \(0.294934\pi\)
\(12\) 0 0
\(13\) 6.74621 1.87106 0.935531 0.353245i \(-0.114922\pi\)
0.935531 + 0.353245i \(0.114922\pi\)
\(14\) 0 0
\(15\) −8.82367 −2.27826
\(16\) 0 0
\(17\) −4.92849 −1.19534 −0.597668 0.801744i \(-0.703906\pi\)
−0.597668 + 0.801744i \(0.703906\pi\)
\(18\) 0 0
\(19\) 1.24680 0.286036 0.143018 0.989720i \(-0.454319\pi\)
0.143018 + 0.989720i \(0.454319\pi\)
\(20\) 0 0
\(21\) −2.18229 −0.476214
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) 11.3484 2.26968
\(26\) 0 0
\(27\) 2.70086 0.519781
\(28\) 0 0
\(29\) 6.48443 1.20413 0.602064 0.798448i \(-0.294345\pi\)
0.602064 + 0.798448i \(0.294345\pi\)
\(30\) 0 0
\(31\) 8.38256 1.50555 0.752776 0.658277i \(-0.228714\pi\)
0.752776 + 0.658277i \(0.228714\pi\)
\(32\) 0 0
\(33\) −8.69387 −1.51341
\(34\) 0 0
\(35\) 4.04332 0.683445
\(36\) 0 0
\(37\) −7.61137 −1.25130 −0.625651 0.780103i \(-0.715167\pi\)
−0.625651 + 0.780103i \(0.715167\pi\)
\(38\) 0 0
\(39\) −14.7222 −2.35743
\(40\) 0 0
\(41\) −7.11078 −1.11052 −0.555259 0.831678i \(-0.687381\pi\)
−0.555259 + 0.831678i \(0.687381\pi\)
\(42\) 0 0
\(43\) 1.11777 0.170458 0.0852291 0.996361i \(-0.472838\pi\)
0.0852291 + 0.996361i \(0.472838\pi\)
\(44\) 0 0
\(45\) 7.12582 1.06225
\(46\) 0 0
\(47\) −8.31426 −1.21276 −0.606380 0.795175i \(-0.707379\pi\)
−0.606380 + 0.795175i \(0.707379\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 10.7554 1.50605
\(52\) 0 0
\(53\) −4.77154 −0.655421 −0.327711 0.944778i \(-0.606277\pi\)
−0.327711 + 0.944778i \(0.606277\pi\)
\(54\) 0 0
\(55\) 16.1079 2.17199
\(56\) 0 0
\(57\) −2.72088 −0.360389
\(58\) 0 0
\(59\) −1.31712 −0.171475 −0.0857373 0.996318i \(-0.527325\pi\)
−0.0857373 + 0.996318i \(0.527325\pi\)
\(60\) 0 0
\(61\) 0.838914 0.107412 0.0537060 0.998557i \(-0.482897\pi\)
0.0537060 + 0.998557i \(0.482897\pi\)
\(62\) 0 0
\(63\) 1.76237 0.222038
\(64\) 0 0
\(65\) 27.2771 3.38330
\(66\) 0 0
\(67\) −12.4350 −1.51918 −0.759591 0.650401i \(-0.774601\pi\)
−0.759591 + 0.650401i \(0.774601\pi\)
\(68\) 0 0
\(69\) −2.18229 −0.262716
\(70\) 0 0
\(71\) −10.0613 −1.19406 −0.597028 0.802220i \(-0.703652\pi\)
−0.597028 + 0.802220i \(0.703652\pi\)
\(72\) 0 0
\(73\) 6.46827 0.757054 0.378527 0.925590i \(-0.376431\pi\)
0.378527 + 0.925590i \(0.376431\pi\)
\(74\) 0 0
\(75\) −24.7655 −2.85967
\(76\) 0 0
\(77\) 3.98384 0.454001
\(78\) 0 0
\(79\) 6.45910 0.726706 0.363353 0.931652i \(-0.381632\pi\)
0.363353 + 0.931652i \(0.381632\pi\)
\(80\) 0 0
\(81\) −11.1812 −1.24235
\(82\) 0 0
\(83\) 5.59303 0.613915 0.306957 0.951723i \(-0.400689\pi\)
0.306957 + 0.951723i \(0.400689\pi\)
\(84\) 0 0
\(85\) −19.9275 −2.16144
\(86\) 0 0
\(87\) −14.1509 −1.51713
\(88\) 0 0
\(89\) −10.2619 −1.08776 −0.543881 0.839162i \(-0.683046\pi\)
−0.543881 + 0.839162i \(0.683046\pi\)
\(90\) 0 0
\(91\) 6.74621 0.707195
\(92\) 0 0
\(93\) −18.2931 −1.89691
\(94\) 0 0
\(95\) 5.04121 0.517217
\(96\) 0 0
\(97\) 11.2477 1.14203 0.571016 0.820939i \(-0.306549\pi\)
0.571016 + 0.820939i \(0.306549\pi\)
\(98\) 0 0
\(99\) 7.02099 0.705636
\(100\) 0 0
\(101\) −13.5690 −1.35016 −0.675082 0.737743i \(-0.735892\pi\)
−0.675082 + 0.737743i \(0.735892\pi\)
\(102\) 0 0
\(103\) −12.4512 −1.22685 −0.613427 0.789752i \(-0.710209\pi\)
−0.613427 + 0.789752i \(0.710209\pi\)
\(104\) 0 0
\(105\) −8.82367 −0.861102
\(106\) 0 0
\(107\) 5.11777 0.494753 0.247377 0.968919i \(-0.420431\pi\)
0.247377 + 0.968919i \(0.420431\pi\)
\(108\) 0 0
\(109\) −3.31509 −0.317528 −0.158764 0.987317i \(-0.550751\pi\)
−0.158764 + 0.987317i \(0.550751\pi\)
\(110\) 0 0
\(111\) 16.6102 1.57657
\(112\) 0 0
\(113\) 13.1721 1.23913 0.619563 0.784947i \(-0.287310\pi\)
0.619563 + 0.784947i \(0.287310\pi\)
\(114\) 0 0
\(115\) 4.04332 0.377041
\(116\) 0 0
\(117\) 11.8893 1.09917
\(118\) 0 0
\(119\) −4.92849 −0.451794
\(120\) 0 0
\(121\) 4.87097 0.442815
\(122\) 0 0
\(123\) 15.5177 1.39919
\(124\) 0 0
\(125\) 25.6686 2.29587
\(126\) 0 0
\(127\) 4.50059 0.399363 0.199682 0.979861i \(-0.436009\pi\)
0.199682 + 0.979861i \(0.436009\pi\)
\(128\) 0 0
\(129\) −2.43929 −0.214768
\(130\) 0 0
\(131\) 1.22882 0.107362 0.0536811 0.998558i \(-0.482905\pi\)
0.0536811 + 0.998558i \(0.482905\pi\)
\(132\) 0 0
\(133\) 1.24680 0.108111
\(134\) 0 0
\(135\) 10.9204 0.939882
\(136\) 0 0
\(137\) 2.61018 0.223003 0.111502 0.993764i \(-0.464434\pi\)
0.111502 + 0.993764i \(0.464434\pi\)
\(138\) 0 0
\(139\) 11.5157 0.976751 0.488375 0.872634i \(-0.337590\pi\)
0.488375 + 0.872634i \(0.337590\pi\)
\(140\) 0 0
\(141\) 18.1441 1.52801
\(142\) 0 0
\(143\) 26.8758 2.24747
\(144\) 0 0
\(145\) 26.2186 2.17734
\(146\) 0 0
\(147\) −2.18229 −0.179992
\(148\) 0 0
\(149\) 6.45120 0.528503 0.264252 0.964454i \(-0.414875\pi\)
0.264252 + 0.964454i \(0.414875\pi\)
\(150\) 0 0
\(151\) −3.22147 −0.262159 −0.131080 0.991372i \(-0.541844\pi\)
−0.131080 + 0.991372i \(0.541844\pi\)
\(152\) 0 0
\(153\) −8.68582 −0.702207
\(154\) 0 0
\(155\) 33.8933 2.72238
\(156\) 0 0
\(157\) −22.2296 −1.77412 −0.887058 0.461658i \(-0.847255\pi\)
−0.887058 + 0.461658i \(0.847255\pi\)
\(158\) 0 0
\(159\) 10.4129 0.825794
\(160\) 0 0
\(161\) 1.00000 0.0788110
\(162\) 0 0
\(163\) −13.1291 −1.02835 −0.514176 0.857685i \(-0.671902\pi\)
−0.514176 + 0.857685i \(0.671902\pi\)
\(164\) 0 0
\(165\) −35.1521 −2.73659
\(166\) 0 0
\(167\) 7.53573 0.583132 0.291566 0.956551i \(-0.405824\pi\)
0.291566 + 0.956551i \(0.405824\pi\)
\(168\) 0 0
\(169\) 32.5113 2.50087
\(170\) 0 0
\(171\) 2.19732 0.168034
\(172\) 0 0
\(173\) −7.24680 −0.550964 −0.275482 0.961306i \(-0.588837\pi\)
−0.275482 + 0.961306i \(0.588837\pi\)
\(174\) 0 0
\(175\) 11.3484 0.857859
\(176\) 0 0
\(177\) 2.87433 0.216048
\(178\) 0 0
\(179\) 8.90113 0.665302 0.332651 0.943050i \(-0.392057\pi\)
0.332651 + 0.943050i \(0.392057\pi\)
\(180\) 0 0
\(181\) 21.8974 1.62762 0.813809 0.581133i \(-0.197390\pi\)
0.813809 + 0.581133i \(0.197390\pi\)
\(182\) 0 0
\(183\) −1.83075 −0.135333
\(184\) 0 0
\(185\) −30.7752 −2.26264
\(186\) 0 0
\(187\) −19.6343 −1.43580
\(188\) 0 0
\(189\) 2.70086 0.196459
\(190\) 0 0
\(191\) 20.3405 1.47179 0.735894 0.677097i \(-0.236762\pi\)
0.735894 + 0.677097i \(0.236762\pi\)
\(192\) 0 0
\(193\) −9.38466 −0.675523 −0.337761 0.941232i \(-0.609670\pi\)
−0.337761 + 0.941232i \(0.609670\pi\)
\(194\) 0 0
\(195\) −59.5263 −4.26277
\(196\) 0 0
\(197\) −21.0544 −1.50006 −0.750032 0.661402i \(-0.769962\pi\)
−0.750032 + 0.661402i \(0.769962\pi\)
\(198\) 0 0
\(199\) 2.99881 0.212580 0.106290 0.994335i \(-0.466103\pi\)
0.106290 + 0.994335i \(0.466103\pi\)
\(200\) 0 0
\(201\) 27.1368 1.91408
\(202\) 0 0
\(203\) 6.48443 0.455118
\(204\) 0 0
\(205\) −28.7511 −2.00807
\(206\) 0 0
\(207\) 1.76237 0.122493
\(208\) 0 0
\(209\) 4.96705 0.343578
\(210\) 0 0
\(211\) 20.2981 1.39738 0.698690 0.715425i \(-0.253767\pi\)
0.698690 + 0.715425i \(0.253767\pi\)
\(212\) 0 0
\(213\) 21.9566 1.50444
\(214\) 0 0
\(215\) 4.51950 0.308227
\(216\) 0 0
\(217\) 8.38256 0.569045
\(218\) 0 0
\(219\) −14.1156 −0.953845
\(220\) 0 0
\(221\) −33.2486 −2.23655
\(222\) 0 0
\(223\) −20.5075 −1.37329 −0.686643 0.726995i \(-0.740917\pi\)
−0.686643 + 0.726995i \(0.740917\pi\)
\(224\) 0 0
\(225\) 20.0001 1.33334
\(226\) 0 0
\(227\) 3.77273 0.250405 0.125202 0.992131i \(-0.460042\pi\)
0.125202 + 0.992131i \(0.460042\pi\)
\(228\) 0 0
\(229\) 3.12217 0.206319 0.103159 0.994665i \(-0.467105\pi\)
0.103159 + 0.994665i \(0.467105\pi\)
\(230\) 0 0
\(231\) −8.69387 −0.572015
\(232\) 0 0
\(233\) 23.8921 1.56522 0.782610 0.622512i \(-0.213888\pi\)
0.782610 + 0.622512i \(0.213888\pi\)
\(234\) 0 0
\(235\) −33.6172 −2.19294
\(236\) 0 0
\(237\) −14.0956 −0.915608
\(238\) 0 0
\(239\) −1.54180 −0.0997311 −0.0498655 0.998756i \(-0.515879\pi\)
−0.0498655 + 0.998756i \(0.515879\pi\)
\(240\) 0 0
\(241\) 12.5639 0.809313 0.404657 0.914469i \(-0.367391\pi\)
0.404657 + 0.914469i \(0.367391\pi\)
\(242\) 0 0
\(243\) 16.2979 1.04551
\(244\) 0 0
\(245\) 4.04332 0.258318
\(246\) 0 0
\(247\) 8.41118 0.535191
\(248\) 0 0
\(249\) −12.2056 −0.773498
\(250\) 0 0
\(251\) −14.4753 −0.913670 −0.456835 0.889551i \(-0.651017\pi\)
−0.456835 + 0.889551i \(0.651017\pi\)
\(252\) 0 0
\(253\) 3.98384 0.250462
\(254\) 0 0
\(255\) 43.4874 2.72329
\(256\) 0 0
\(257\) 12.5125 0.780509 0.390254 0.920707i \(-0.372387\pi\)
0.390254 + 0.920707i \(0.372387\pi\)
\(258\) 0 0
\(259\) −7.61137 −0.472948
\(260\) 0 0
\(261\) 11.4280 0.707373
\(262\) 0 0
\(263\) 19.7242 1.21625 0.608124 0.793842i \(-0.291922\pi\)
0.608124 + 0.793842i \(0.291922\pi\)
\(264\) 0 0
\(265\) −19.2928 −1.18515
\(266\) 0 0
\(267\) 22.3945 1.37052
\(268\) 0 0
\(269\) 1.86398 0.113649 0.0568244 0.998384i \(-0.481902\pi\)
0.0568244 + 0.998384i \(0.481902\pi\)
\(270\) 0 0
\(271\) −6.47729 −0.393467 −0.196734 0.980457i \(-0.563033\pi\)
−0.196734 + 0.980457i \(0.563033\pi\)
\(272\) 0 0
\(273\) −14.7222 −0.891025
\(274\) 0 0
\(275\) 45.2102 2.72628
\(276\) 0 0
\(277\) 26.1077 1.56866 0.784330 0.620343i \(-0.213007\pi\)
0.784330 + 0.620343i \(0.213007\pi\)
\(278\) 0 0
\(279\) 14.7732 0.884446
\(280\) 0 0
\(281\) 3.12784 0.186592 0.0932958 0.995638i \(-0.470260\pi\)
0.0932958 + 0.995638i \(0.470260\pi\)
\(282\) 0 0
\(283\) −21.4017 −1.27220 −0.636100 0.771606i \(-0.719454\pi\)
−0.636100 + 0.771606i \(0.719454\pi\)
\(284\) 0 0
\(285\) −11.0014 −0.651664
\(286\) 0 0
\(287\) −7.11078 −0.419736
\(288\) 0 0
\(289\) 7.29004 0.428826
\(290\) 0 0
\(291\) −24.5457 −1.43890
\(292\) 0 0
\(293\) −20.7743 −1.21365 −0.606823 0.794837i \(-0.707556\pi\)
−0.606823 + 0.794837i \(0.707556\pi\)
\(294\) 0 0
\(295\) −5.32554 −0.310065
\(296\) 0 0
\(297\) 10.7598 0.624347
\(298\) 0 0
\(299\) 6.74621 0.390143
\(300\) 0 0
\(301\) 1.11777 0.0644272
\(302\) 0 0
\(303\) 29.6114 1.70113
\(304\) 0 0
\(305\) 3.39199 0.194225
\(306\) 0 0
\(307\) −6.95787 −0.397107 −0.198553 0.980090i \(-0.563624\pi\)
−0.198553 + 0.980090i \(0.563624\pi\)
\(308\) 0 0
\(309\) 27.1721 1.54577
\(310\) 0 0
\(311\) −31.5759 −1.79051 −0.895253 0.445558i \(-0.853005\pi\)
−0.895253 + 0.445558i \(0.853005\pi\)
\(312\) 0 0
\(313\) −7.00505 −0.395949 −0.197974 0.980207i \(-0.563436\pi\)
−0.197974 + 0.980207i \(0.563436\pi\)
\(314\) 0 0
\(315\) 7.12582 0.401494
\(316\) 0 0
\(317\) 21.2749 1.19492 0.597458 0.801900i \(-0.296177\pi\)
0.597458 + 0.801900i \(0.296177\pi\)
\(318\) 0 0
\(319\) 25.8329 1.44637
\(320\) 0 0
\(321\) −11.1684 −0.623361
\(322\) 0 0
\(323\) −6.14485 −0.341909
\(324\) 0 0
\(325\) 76.5587 4.24671
\(326\) 0 0
\(327\) 7.23448 0.400068
\(328\) 0 0
\(329\) −8.31426 −0.458380
\(330\) 0 0
\(331\) −22.9759 −1.26287 −0.631434 0.775430i \(-0.717533\pi\)
−0.631434 + 0.775430i \(0.717533\pi\)
\(332\) 0 0
\(333\) −13.4140 −0.735085
\(334\) 0 0
\(335\) −50.2788 −2.74702
\(336\) 0 0
\(337\) −1.62145 −0.0883258 −0.0441629 0.999024i \(-0.514062\pi\)
−0.0441629 + 0.999024i \(0.514062\pi\)
\(338\) 0 0
\(339\) −28.7452 −1.56123
\(340\) 0 0
\(341\) 33.3947 1.80843
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) −8.82367 −0.475050
\(346\) 0 0
\(347\) 3.01310 0.161752 0.0808758 0.996724i \(-0.474228\pi\)
0.0808758 + 0.996724i \(0.474228\pi\)
\(348\) 0 0
\(349\) 3.83992 0.205546 0.102773 0.994705i \(-0.467228\pi\)
0.102773 + 0.994705i \(0.467228\pi\)
\(350\) 0 0
\(351\) 18.2206 0.972543
\(352\) 0 0
\(353\) −33.8459 −1.80144 −0.900719 0.434403i \(-0.856960\pi\)
−0.900719 + 0.434403i \(0.856960\pi\)
\(354\) 0 0
\(355\) −40.6810 −2.15912
\(356\) 0 0
\(357\) 10.7554 0.569235
\(358\) 0 0
\(359\) −14.1147 −0.744946 −0.372473 0.928043i \(-0.621490\pi\)
−0.372473 + 0.928043i \(0.621490\pi\)
\(360\) 0 0
\(361\) −17.4455 −0.918184
\(362\) 0 0
\(363\) −10.6298 −0.557922
\(364\) 0 0
\(365\) 26.1533 1.36892
\(366\) 0 0
\(367\) −26.7917 −1.39852 −0.699258 0.714869i \(-0.746486\pi\)
−0.699258 + 0.714869i \(0.746486\pi\)
\(368\) 0 0
\(369\) −12.5318 −0.652380
\(370\) 0 0
\(371\) −4.77154 −0.247726
\(372\) 0 0
\(373\) 10.9931 0.569201 0.284600 0.958646i \(-0.408139\pi\)
0.284600 + 0.958646i \(0.408139\pi\)
\(374\) 0 0
\(375\) −56.0163 −2.89267
\(376\) 0 0
\(377\) 43.7453 2.25300
\(378\) 0 0
\(379\) 0.280117 0.0143886 0.00719431 0.999974i \(-0.497710\pi\)
0.00719431 + 0.999974i \(0.497710\pi\)
\(380\) 0 0
\(381\) −9.82158 −0.503175
\(382\) 0 0
\(383\) 11.3817 0.581579 0.290789 0.956787i \(-0.406082\pi\)
0.290789 + 0.956787i \(0.406082\pi\)
\(384\) 0 0
\(385\) 16.1079 0.820936
\(386\) 0 0
\(387\) 1.96992 0.100137
\(388\) 0 0
\(389\) −0.129032 −0.00654216 −0.00327108 0.999995i \(-0.501041\pi\)
−0.00327108 + 0.999995i \(0.501041\pi\)
\(390\) 0 0
\(391\) −4.92849 −0.249245
\(392\) 0 0
\(393\) −2.68163 −0.135270
\(394\) 0 0
\(395\) 26.1162 1.31405
\(396\) 0 0
\(397\) 2.48225 0.124581 0.0622903 0.998058i \(-0.480160\pi\)
0.0622903 + 0.998058i \(0.480160\pi\)
\(398\) 0 0
\(399\) −2.72088 −0.136214
\(400\) 0 0
\(401\) −12.0843 −0.603459 −0.301730 0.953394i \(-0.597564\pi\)
−0.301730 + 0.953394i \(0.597564\pi\)
\(402\) 0 0
\(403\) 56.5505 2.81698
\(404\) 0 0
\(405\) −45.2090 −2.24645
\(406\) 0 0
\(407\) −30.3225 −1.50303
\(408\) 0 0
\(409\) −4.32161 −0.213690 −0.106845 0.994276i \(-0.534075\pi\)
−0.106845 + 0.994276i \(0.534075\pi\)
\(410\) 0 0
\(411\) −5.69617 −0.280971
\(412\) 0 0
\(413\) −1.31712 −0.0648113
\(414\) 0 0
\(415\) 22.6144 1.11010
\(416\) 0 0
\(417\) −25.1306 −1.23065
\(418\) 0 0
\(419\) 20.0044 0.977277 0.488638 0.872486i \(-0.337494\pi\)
0.488638 + 0.872486i \(0.337494\pi\)
\(420\) 0 0
\(421\) 27.4017 1.33548 0.667739 0.744395i \(-0.267262\pi\)
0.667739 + 0.744395i \(0.267262\pi\)
\(422\) 0 0
\(423\) −14.6528 −0.712444
\(424\) 0 0
\(425\) −55.9306 −2.71303
\(426\) 0 0
\(427\) 0.838914 0.0405979
\(428\) 0 0
\(429\) −58.6507 −2.83168
\(430\) 0 0
\(431\) 16.4571 0.792710 0.396355 0.918097i \(-0.370275\pi\)
0.396355 + 0.918097i \(0.370275\pi\)
\(432\) 0 0
\(433\) −4.63332 −0.222663 −0.111332 0.993783i \(-0.535512\pi\)
−0.111332 + 0.993783i \(0.535512\pi\)
\(434\) 0 0
\(435\) −57.2165 −2.74332
\(436\) 0 0
\(437\) 1.24680 0.0596426
\(438\) 0 0
\(439\) −25.6359 −1.22354 −0.611769 0.791037i \(-0.709542\pi\)
−0.611769 + 0.791037i \(0.709542\pi\)
\(440\) 0 0
\(441\) 1.76237 0.0839223
\(442\) 0 0
\(443\) −9.07846 −0.431330 −0.215665 0.976467i \(-0.569192\pi\)
−0.215665 + 0.976467i \(0.569192\pi\)
\(444\) 0 0
\(445\) −41.4922 −1.96692
\(446\) 0 0
\(447\) −14.0784 −0.665884
\(448\) 0 0
\(449\) 28.6206 1.35069 0.675346 0.737501i \(-0.263995\pi\)
0.675346 + 0.737501i \(0.263995\pi\)
\(450\) 0 0
\(451\) −28.3282 −1.33392
\(452\) 0 0
\(453\) 7.03016 0.330306
\(454\) 0 0
\(455\) 27.2771 1.27877
\(456\) 0 0
\(457\) 2.79560 0.130773 0.0653863 0.997860i \(-0.479172\pi\)
0.0653863 + 0.997860i \(0.479172\pi\)
\(458\) 0 0
\(459\) −13.3112 −0.621313
\(460\) 0 0
\(461\) −10.1360 −0.472082 −0.236041 0.971743i \(-0.575850\pi\)
−0.236041 + 0.971743i \(0.575850\pi\)
\(462\) 0 0
\(463\) −11.6273 −0.540368 −0.270184 0.962809i \(-0.587085\pi\)
−0.270184 + 0.962809i \(0.587085\pi\)
\(464\) 0 0
\(465\) −73.9649 −3.43004
\(466\) 0 0
\(467\) −36.9748 −1.71099 −0.855494 0.517813i \(-0.826746\pi\)
−0.855494 + 0.517813i \(0.826746\pi\)
\(468\) 0 0
\(469\) −12.4350 −0.574197
\(470\) 0 0
\(471\) 48.5113 2.23528
\(472\) 0 0
\(473\) 4.45301 0.204750
\(474\) 0 0
\(475\) 14.1492 0.649210
\(476\) 0 0
\(477\) −8.40921 −0.385032
\(478\) 0 0
\(479\) 10.8039 0.493641 0.246821 0.969061i \(-0.420614\pi\)
0.246821 + 0.969061i \(0.420614\pi\)
\(480\) 0 0
\(481\) −51.3479 −2.34126
\(482\) 0 0
\(483\) −2.18229 −0.0992974
\(484\) 0 0
\(485\) 45.4781 2.06505
\(486\) 0 0
\(487\) 33.5054 1.51828 0.759138 0.650930i \(-0.225621\pi\)
0.759138 + 0.650930i \(0.225621\pi\)
\(488\) 0 0
\(489\) 28.6515 1.29566
\(490\) 0 0
\(491\) −31.8118 −1.43565 −0.717823 0.696226i \(-0.754861\pi\)
−0.717823 + 0.696226i \(0.754861\pi\)
\(492\) 0 0
\(493\) −31.9585 −1.43934
\(494\) 0 0
\(495\) 28.3881 1.27595
\(496\) 0 0
\(497\) −10.0613 −0.451311
\(498\) 0 0
\(499\) −8.24689 −0.369181 −0.184591 0.982815i \(-0.559096\pi\)
−0.184591 + 0.982815i \(0.559096\pi\)
\(500\) 0 0
\(501\) −16.4451 −0.734714
\(502\) 0 0
\(503\) 16.6968 0.744474 0.372237 0.928138i \(-0.378591\pi\)
0.372237 + 0.928138i \(0.378591\pi\)
\(504\) 0 0
\(505\) −54.8637 −2.44140
\(506\) 0 0
\(507\) −70.9490 −3.15095
\(508\) 0 0
\(509\) −12.0106 −0.532362 −0.266181 0.963923i \(-0.585762\pi\)
−0.266181 + 0.963923i \(0.585762\pi\)
\(510\) 0 0
\(511\) 6.46827 0.286139
\(512\) 0 0
\(513\) 3.36744 0.148676
\(514\) 0 0
\(515\) −50.3442 −2.21843
\(516\) 0 0
\(517\) −33.1227 −1.45673
\(518\) 0 0
\(519\) 15.8146 0.694183
\(520\) 0 0
\(521\) −3.19522 −0.139985 −0.0699925 0.997548i \(-0.522298\pi\)
−0.0699925 + 0.997548i \(0.522298\pi\)
\(522\) 0 0
\(523\) 19.2569 0.842044 0.421022 0.907050i \(-0.361671\pi\)
0.421022 + 0.907050i \(0.361671\pi\)
\(524\) 0 0
\(525\) −24.7655 −1.08085
\(526\) 0 0
\(527\) −41.3134 −1.79964
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −2.32125 −0.100734
\(532\) 0 0
\(533\) −47.9708 −2.07785
\(534\) 0 0
\(535\) 20.6928 0.894626
\(536\) 0 0
\(537\) −19.4248 −0.838243
\(538\) 0 0
\(539\) 3.98384 0.171596
\(540\) 0 0
\(541\) 21.7131 0.933518 0.466759 0.884385i \(-0.345422\pi\)
0.466759 + 0.884385i \(0.345422\pi\)
\(542\) 0 0
\(543\) −47.7863 −2.05071
\(544\) 0 0
\(545\) −13.4040 −0.574163
\(546\) 0 0
\(547\) 23.9565 1.02431 0.512153 0.858894i \(-0.328848\pi\)
0.512153 + 0.858894i \(0.328848\pi\)
\(548\) 0 0
\(549\) 1.47848 0.0630998
\(550\) 0 0
\(551\) 8.08480 0.344424
\(552\) 0 0
\(553\) 6.45910 0.274669
\(554\) 0 0
\(555\) 67.1602 2.85079
\(556\) 0 0
\(557\) −17.7727 −0.753055 −0.376527 0.926406i \(-0.622882\pi\)
−0.376527 + 0.926406i \(0.622882\pi\)
\(558\) 0 0
\(559\) 7.54071 0.318938
\(560\) 0 0
\(561\) 42.8477 1.80903
\(562\) 0 0
\(563\) −29.4443 −1.24093 −0.620465 0.784234i \(-0.713056\pi\)
−0.620465 + 0.784234i \(0.713056\pi\)
\(564\) 0 0
\(565\) 53.2589 2.24062
\(566\) 0 0
\(567\) −11.1812 −0.469565
\(568\) 0 0
\(569\) 3.12604 0.131050 0.0655251 0.997851i \(-0.479128\pi\)
0.0655251 + 0.997851i \(0.479128\pi\)
\(570\) 0 0
\(571\) −15.3393 −0.641931 −0.320965 0.947091i \(-0.604007\pi\)
−0.320965 + 0.947091i \(0.604007\pi\)
\(572\) 0 0
\(573\) −44.3888 −1.85437
\(574\) 0 0
\(575\) 11.3484 0.473261
\(576\) 0 0
\(577\) 35.9790 1.49783 0.748913 0.662668i \(-0.230576\pi\)
0.748913 + 0.662668i \(0.230576\pi\)
\(578\) 0 0
\(579\) 20.4800 0.851120
\(580\) 0 0
\(581\) 5.59303 0.232038
\(582\) 0 0
\(583\) −19.0090 −0.787274
\(584\) 0 0
\(585\) 48.0722 1.98754
\(586\) 0 0
\(587\) −7.42319 −0.306388 −0.153194 0.988196i \(-0.548956\pi\)
−0.153194 + 0.988196i \(0.548956\pi\)
\(588\) 0 0
\(589\) 10.4514 0.430642
\(590\) 0 0
\(591\) 45.9467 1.88999
\(592\) 0 0
\(593\) −9.96768 −0.409323 −0.204662 0.978833i \(-0.565609\pi\)
−0.204662 + 0.978833i \(0.565609\pi\)
\(594\) 0 0
\(595\) −19.9275 −0.816946
\(596\) 0 0
\(597\) −6.54427 −0.267839
\(598\) 0 0
\(599\) −10.6126 −0.433617 −0.216809 0.976214i \(-0.569565\pi\)
−0.216809 + 0.976214i \(0.569565\pi\)
\(600\) 0 0
\(601\) −31.2158 −1.27332 −0.636659 0.771146i \(-0.719684\pi\)
−0.636659 + 0.771146i \(0.719684\pi\)
\(602\) 0 0
\(603\) −21.9151 −0.892453
\(604\) 0 0
\(605\) 19.6949 0.800710
\(606\) 0 0
\(607\) 17.9603 0.728987 0.364494 0.931206i \(-0.381242\pi\)
0.364494 + 0.931206i \(0.381242\pi\)
\(608\) 0 0
\(609\) −14.1509 −0.573423
\(610\) 0 0
\(611\) −56.0897 −2.26915
\(612\) 0 0
\(613\) 20.1209 0.812677 0.406339 0.913723i \(-0.366805\pi\)
0.406339 + 0.913723i \(0.366805\pi\)
\(614\) 0 0
\(615\) 62.7432 2.53005
\(616\) 0 0
\(617\) −26.3689 −1.06157 −0.530787 0.847506i \(-0.678103\pi\)
−0.530787 + 0.847506i \(0.678103\pi\)
\(618\) 0 0
\(619\) 35.6959 1.43474 0.717370 0.696692i \(-0.245346\pi\)
0.717370 + 0.696692i \(0.245346\pi\)
\(620\) 0 0
\(621\) 2.70086 0.108382
\(622\) 0 0
\(623\) −10.2619 −0.411135
\(624\) 0 0
\(625\) 47.0443 1.88177
\(626\) 0 0
\(627\) −10.8395 −0.432889
\(628\) 0 0
\(629\) 37.5126 1.49573
\(630\) 0 0
\(631\) 8.26178 0.328896 0.164448 0.986386i \(-0.447416\pi\)
0.164448 + 0.986386i \(0.447416\pi\)
\(632\) 0 0
\(633\) −44.2963 −1.76062
\(634\) 0 0
\(635\) 18.1973 0.722139
\(636\) 0 0
\(637\) 6.74621 0.267294
\(638\) 0 0
\(639\) −17.7317 −0.701456
\(640\) 0 0
\(641\) 7.85518 0.310261 0.155130 0.987894i \(-0.450420\pi\)
0.155130 + 0.987894i \(0.450420\pi\)
\(642\) 0 0
\(643\) −14.9907 −0.591176 −0.295588 0.955315i \(-0.595516\pi\)
−0.295588 + 0.955315i \(0.595516\pi\)
\(644\) 0 0
\(645\) −9.86283 −0.388349
\(646\) 0 0
\(647\) −16.1310 −0.634177 −0.317088 0.948396i \(-0.602705\pi\)
−0.317088 + 0.948396i \(0.602705\pi\)
\(648\) 0 0
\(649\) −5.24720 −0.205971
\(650\) 0 0
\(651\) −18.2931 −0.716964
\(652\) 0 0
\(653\) −7.15080 −0.279833 −0.139916 0.990163i \(-0.544683\pi\)
−0.139916 + 0.990163i \(0.544683\pi\)
\(654\) 0 0
\(655\) 4.96849 0.194135
\(656\) 0 0
\(657\) 11.3995 0.444736
\(658\) 0 0
\(659\) −27.7646 −1.08156 −0.540778 0.841165i \(-0.681870\pi\)
−0.540778 + 0.841165i \(0.681870\pi\)
\(660\) 0 0
\(661\) −0.707812 −0.0275307 −0.0137653 0.999905i \(-0.504382\pi\)
−0.0137653 + 0.999905i \(0.504382\pi\)
\(662\) 0 0
\(663\) 72.5580 2.81792
\(664\) 0 0
\(665\) 5.04121 0.195490
\(666\) 0 0
\(667\) 6.48443 0.251078
\(668\) 0 0
\(669\) 44.7533 1.73026
\(670\) 0 0
\(671\) 3.34210 0.129020
\(672\) 0 0
\(673\) −8.96378 −0.345528 −0.172764 0.984963i \(-0.555270\pi\)
−0.172764 + 0.984963i \(0.555270\pi\)
\(674\) 0 0
\(675\) 30.6505 1.17974
\(676\) 0 0
\(677\) −46.2685 −1.77824 −0.889122 0.457671i \(-0.848684\pi\)
−0.889122 + 0.457671i \(0.848684\pi\)
\(678\) 0 0
\(679\) 11.2477 0.431648
\(680\) 0 0
\(681\) −8.23317 −0.315496
\(682\) 0 0
\(683\) 18.6674 0.714289 0.357145 0.934049i \(-0.383750\pi\)
0.357145 + 0.934049i \(0.383750\pi\)
\(684\) 0 0
\(685\) 10.5538 0.403240
\(686\) 0 0
\(687\) −6.81347 −0.259950
\(688\) 0 0
\(689\) −32.1898 −1.22633
\(690\) 0 0
\(691\) −47.2398 −1.79709 −0.898543 0.438886i \(-0.855373\pi\)
−0.898543 + 0.438886i \(0.855373\pi\)
\(692\) 0 0
\(693\) 7.02099 0.266706
\(694\) 0 0
\(695\) 46.5617 1.76619
\(696\) 0 0
\(697\) 35.0454 1.32744
\(698\) 0 0
\(699\) −52.1393 −1.97209
\(700\) 0 0
\(701\) −32.8765 −1.24173 −0.620864 0.783918i \(-0.713218\pi\)
−0.620864 + 0.783918i \(0.713218\pi\)
\(702\) 0 0
\(703\) −9.48987 −0.357917
\(704\) 0 0
\(705\) 73.3623 2.76298
\(706\) 0 0
\(707\) −13.5690 −0.510314
\(708\) 0 0
\(709\) 25.3234 0.951039 0.475519 0.879705i \(-0.342260\pi\)
0.475519 + 0.879705i \(0.342260\pi\)
\(710\) 0 0
\(711\) 11.3833 0.426908
\(712\) 0 0
\(713\) 8.38256 0.313929
\(714\) 0 0
\(715\) 108.667 4.06393
\(716\) 0 0
\(717\) 3.36466 0.125655
\(718\) 0 0
\(719\) 3.48142 0.129835 0.0649176 0.997891i \(-0.479322\pi\)
0.0649176 + 0.997891i \(0.479322\pi\)
\(720\) 0 0
\(721\) −12.4512 −0.463707
\(722\) 0 0
\(723\) −27.4181 −1.01969
\(724\) 0 0
\(725\) 73.5880 2.73299
\(726\) 0 0
\(727\) −14.9789 −0.555538 −0.277769 0.960648i \(-0.589595\pi\)
−0.277769 + 0.960648i \(0.589595\pi\)
\(728\) 0 0
\(729\) −2.02317 −0.0749324
\(730\) 0 0
\(731\) −5.50892 −0.203755
\(732\) 0 0
\(733\) 40.6230 1.50045 0.750223 0.661185i \(-0.229946\pi\)
0.750223 + 0.661185i \(0.229946\pi\)
\(734\) 0 0
\(735\) −8.82367 −0.325466
\(736\) 0 0
\(737\) −49.5392 −1.82480
\(738\) 0 0
\(739\) −15.5537 −0.572153 −0.286076 0.958207i \(-0.592351\pi\)
−0.286076 + 0.958207i \(0.592351\pi\)
\(740\) 0 0
\(741\) −18.3556 −0.674310
\(742\) 0 0
\(743\) −1.02324 −0.0375390 −0.0187695 0.999824i \(-0.505975\pi\)
−0.0187695 + 0.999824i \(0.505975\pi\)
\(744\) 0 0
\(745\) 26.0843 0.955653
\(746\) 0 0
\(747\) 9.85699 0.360648
\(748\) 0 0
\(749\) 5.11777 0.186999
\(750\) 0 0
\(751\) 20.1696 0.735997 0.367999 0.929826i \(-0.380043\pi\)
0.367999 + 0.929826i \(0.380043\pi\)
\(752\) 0 0
\(753\) 31.5892 1.15117
\(754\) 0 0
\(755\) −13.0254 −0.474044
\(756\) 0 0
\(757\) −10.4310 −0.379122 −0.189561 0.981869i \(-0.560706\pi\)
−0.189561 + 0.981869i \(0.560706\pi\)
\(758\) 0 0
\(759\) −8.69387 −0.315568
\(760\) 0 0
\(761\) 5.80967 0.210600 0.105300 0.994440i \(-0.466420\pi\)
0.105300 + 0.994440i \(0.466420\pi\)
\(762\) 0 0
\(763\) −3.31509 −0.120014
\(764\) 0 0
\(765\) −35.1195 −1.26975
\(766\) 0 0
\(767\) −8.88557 −0.320839
\(768\) 0 0
\(769\) 35.3898 1.27619 0.638094 0.769959i \(-0.279723\pi\)
0.638094 + 0.769959i \(0.279723\pi\)
\(770\) 0 0
\(771\) −27.3059 −0.983396
\(772\) 0 0
\(773\) −28.5275 −1.02606 −0.513032 0.858369i \(-0.671478\pi\)
−0.513032 + 0.858369i \(0.671478\pi\)
\(774\) 0 0
\(775\) 95.1287 3.41712
\(776\) 0 0
\(777\) 16.6102 0.595887
\(778\) 0 0
\(779\) −8.86573 −0.317648
\(780\) 0 0
\(781\) −40.0826 −1.43427
\(782\) 0 0
\(783\) 17.5136 0.625884
\(784\) 0 0
\(785\) −89.8813 −3.20800
\(786\) 0 0
\(787\) 25.8412 0.921139 0.460570 0.887624i \(-0.347645\pi\)
0.460570 + 0.887624i \(0.347645\pi\)
\(788\) 0 0
\(789\) −43.0439 −1.53240
\(790\) 0 0
\(791\) 13.1721 0.468345
\(792\) 0 0
\(793\) 5.65949 0.200974
\(794\) 0 0
\(795\) 42.1025 1.49322
\(796\) 0 0
\(797\) −32.9288 −1.16640 −0.583199 0.812329i \(-0.698199\pi\)
−0.583199 + 0.812329i \(0.698199\pi\)
\(798\) 0 0
\(799\) 40.9768 1.44965
\(800\) 0 0
\(801\) −18.0853 −0.639013
\(802\) 0 0
\(803\) 25.7685 0.909352
\(804\) 0 0
\(805\) 4.04332 0.142508
\(806\) 0 0
\(807\) −4.06773 −0.143191
\(808\) 0 0
\(809\) −22.7087 −0.798396 −0.399198 0.916865i \(-0.630711\pi\)
−0.399198 + 0.916865i \(0.630711\pi\)
\(810\) 0 0
\(811\) −53.2167 −1.86869 −0.934345 0.356370i \(-0.884014\pi\)
−0.934345 + 0.356370i \(0.884014\pi\)
\(812\) 0 0
\(813\) 14.1353 0.495746
\(814\) 0 0
\(815\) −53.0852 −1.85949
\(816\) 0 0
\(817\) 1.39364 0.0487572
\(818\) 0 0
\(819\) 11.8893 0.415446
\(820\) 0 0
\(821\) 9.09572 0.317443 0.158721 0.987323i \(-0.449263\pi\)
0.158721 + 0.987323i \(0.449263\pi\)
\(822\) 0 0
\(823\) −18.7581 −0.653867 −0.326933 0.945047i \(-0.606015\pi\)
−0.326933 + 0.945047i \(0.606015\pi\)
\(824\) 0 0
\(825\) −98.6616 −3.43496
\(826\) 0 0
\(827\) 18.9647 0.659467 0.329733 0.944074i \(-0.393041\pi\)
0.329733 + 0.944074i \(0.393041\pi\)
\(828\) 0 0
\(829\) 34.1733 1.18689 0.593443 0.804876i \(-0.297768\pi\)
0.593443 + 0.804876i \(0.297768\pi\)
\(830\) 0 0
\(831\) −56.9745 −1.97642
\(832\) 0 0
\(833\) −4.92849 −0.170762
\(834\) 0 0
\(835\) 30.4694 1.05444
\(836\) 0 0
\(837\) 22.6401 0.782558
\(838\) 0 0
\(839\) 43.0050 1.48470 0.742349 0.670014i \(-0.233712\pi\)
0.742349 + 0.670014i \(0.233712\pi\)
\(840\) 0 0
\(841\) 13.0479 0.449926
\(842\) 0 0
\(843\) −6.82585 −0.235095
\(844\) 0 0
\(845\) 131.454 4.52214
\(846\) 0 0
\(847\) 4.87097 0.167368
\(848\) 0 0
\(849\) 46.7047 1.60290
\(850\) 0 0
\(851\) −7.61137 −0.260914
\(852\) 0 0
\(853\) −40.3790 −1.38255 −0.691275 0.722591i \(-0.742951\pi\)
−0.691275 + 0.722591i \(0.742951\pi\)
\(854\) 0 0
\(855\) 8.88448 0.303843
\(856\) 0 0
\(857\) −29.6044 −1.01127 −0.505633 0.862749i \(-0.668741\pi\)
−0.505633 + 0.862749i \(0.668741\pi\)
\(858\) 0 0
\(859\) 15.6912 0.535378 0.267689 0.963505i \(-0.413740\pi\)
0.267689 + 0.963505i \(0.413740\pi\)
\(860\) 0 0
\(861\) 15.5177 0.528843
\(862\) 0 0
\(863\) 18.2405 0.620912 0.310456 0.950588i \(-0.399518\pi\)
0.310456 + 0.950588i \(0.399518\pi\)
\(864\) 0 0
\(865\) −29.3011 −0.996268
\(866\) 0 0
\(867\) −15.9090 −0.540296
\(868\) 0 0
\(869\) 25.7320 0.872899
\(870\) 0 0
\(871\) −83.8894 −2.84248
\(872\) 0 0
\(873\) 19.8226 0.670895
\(874\) 0 0
\(875\) 25.6686 0.867758
\(876\) 0 0
\(877\) −30.2155 −1.02030 −0.510152 0.860084i \(-0.670411\pi\)
−0.510152 + 0.860084i \(0.670411\pi\)
\(878\) 0 0
\(879\) 45.3354 1.52912
\(880\) 0 0
\(881\) 0.443129 0.0149294 0.00746471 0.999972i \(-0.497624\pi\)
0.00746471 + 0.999972i \(0.497624\pi\)
\(882\) 0 0
\(883\) 33.9979 1.14412 0.572061 0.820211i \(-0.306144\pi\)
0.572061 + 0.820211i \(0.306144\pi\)
\(884\) 0 0
\(885\) 11.6218 0.390664
\(886\) 0 0
\(887\) −55.1449 −1.85158 −0.925792 0.378033i \(-0.876601\pi\)
−0.925792 + 0.378033i \(0.876601\pi\)
\(888\) 0 0
\(889\) 4.50059 0.150945
\(890\) 0 0
\(891\) −44.5439 −1.49228
\(892\) 0 0
\(893\) −10.3662 −0.346893
\(894\) 0 0
\(895\) 35.9901 1.20302
\(896\) 0 0
\(897\) −14.7222 −0.491558
\(898\) 0 0
\(899\) 54.3561 1.81288
\(900\) 0 0
\(901\) 23.5165 0.783448
\(902\) 0 0
\(903\) −2.43929 −0.0811746
\(904\) 0 0
\(905\) 88.5379 2.94310
\(906\) 0 0
\(907\) 13.0471 0.433222 0.216611 0.976258i \(-0.430500\pi\)
0.216611 + 0.976258i \(0.430500\pi\)
\(908\) 0 0
\(909\) −23.9135 −0.793162
\(910\) 0 0
\(911\) −4.86610 −0.161221 −0.0806105 0.996746i \(-0.525687\pi\)
−0.0806105 + 0.996746i \(0.525687\pi\)
\(912\) 0 0
\(913\) 22.2817 0.737418
\(914\) 0 0
\(915\) −7.40230 −0.244712
\(916\) 0 0
\(917\) 1.22882 0.0405791
\(918\) 0 0
\(919\) 0.0102695 0.000338761 0 0.000169381 1.00000i \(-0.499946\pi\)
0.000169381 1.00000i \(0.499946\pi\)
\(920\) 0 0
\(921\) 15.1841 0.500332
\(922\) 0 0
\(923\) −67.8756 −2.23415
\(924\) 0 0
\(925\) −86.3770 −2.84006
\(926\) 0 0
\(927\) −21.9436 −0.720723
\(928\) 0 0
\(929\) 13.4689 0.441901 0.220950 0.975285i \(-0.429084\pi\)
0.220950 + 0.975285i \(0.429084\pi\)
\(930\) 0 0
\(931\) 1.24680 0.0408623
\(932\) 0 0
\(933\) 68.9077 2.25594
\(934\) 0 0
\(935\) −79.3878 −2.59626
\(936\) 0 0
\(937\) 23.3740 0.763595 0.381797 0.924246i \(-0.375305\pi\)
0.381797 + 0.924246i \(0.375305\pi\)
\(938\) 0 0
\(939\) 15.2870 0.498873
\(940\) 0 0
\(941\) 34.1588 1.11354 0.556772 0.830665i \(-0.312040\pi\)
0.556772 + 0.830665i \(0.312040\pi\)
\(942\) 0 0
\(943\) −7.11078 −0.231559
\(944\) 0 0
\(945\) 10.9204 0.355242
\(946\) 0 0
\(947\) 25.1775 0.818160 0.409080 0.912499i \(-0.365850\pi\)
0.409080 + 0.912499i \(0.365850\pi\)
\(948\) 0 0
\(949\) 43.6363 1.41649
\(950\) 0 0
\(951\) −46.4278 −1.50553
\(952\) 0 0
\(953\) −26.3000 −0.851939 −0.425969 0.904738i \(-0.640067\pi\)
−0.425969 + 0.904738i \(0.640067\pi\)
\(954\) 0 0
\(955\) 82.2431 2.66133
\(956\) 0 0
\(957\) −56.3748 −1.82234
\(958\) 0 0
\(959\) 2.61018 0.0842873
\(960\) 0 0
\(961\) 39.2672 1.26668
\(962\) 0 0
\(963\) 9.01940 0.290646
\(964\) 0 0
\(965\) −37.9452 −1.22150
\(966\) 0 0
\(967\) −40.9316 −1.31627 −0.658135 0.752900i \(-0.728654\pi\)
−0.658135 + 0.752900i \(0.728654\pi\)
\(968\) 0 0
\(969\) 13.4098 0.430785
\(970\) 0 0
\(971\) −5.65729 −0.181551 −0.0907755 0.995871i \(-0.528935\pi\)
−0.0907755 + 0.995871i \(0.528935\pi\)
\(972\) 0 0
\(973\) 11.5157 0.369177
\(974\) 0 0
\(975\) −167.073 −5.35062
\(976\) 0 0
\(977\) 42.5639 1.36174 0.680870 0.732405i \(-0.261602\pi\)
0.680870 + 0.732405i \(0.261602\pi\)
\(978\) 0 0
\(979\) −40.8819 −1.30659
\(980\) 0 0
\(981\) −5.84242 −0.186534
\(982\) 0 0
\(983\) −31.7904 −1.01395 −0.506977 0.861959i \(-0.669237\pi\)
−0.506977 + 0.861959i \(0.669237\pi\)
\(984\) 0 0
\(985\) −85.1296 −2.71245
\(986\) 0 0
\(987\) 18.1441 0.577533
\(988\) 0 0
\(989\) 1.11777 0.0355430
\(990\) 0 0
\(991\) 56.0238 1.77966 0.889828 0.456297i \(-0.150824\pi\)
0.889828 + 0.456297i \(0.150824\pi\)
\(992\) 0 0
\(993\) 50.1399 1.59114
\(994\) 0 0
\(995\) 12.1252 0.384393
\(996\) 0 0
\(997\) 50.3201 1.59365 0.796827 0.604208i \(-0.206510\pi\)
0.796827 + 0.604208i \(0.206510\pi\)
\(998\) 0 0
\(999\) −20.5573 −0.650403
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 2576.2.a.bb.1.2 5
4.3 odd 2 644.2.a.d.1.4 5
12.11 even 2 5796.2.a.t.1.1 5
28.27 even 2 4508.2.a.f.1.2 5
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
644.2.a.d.1.4 5 4.3 odd 2
2576.2.a.bb.1.2 5 1.1 even 1 trivial
4508.2.a.f.1.2 5 28.27 even 2
5796.2.a.t.1.1 5 12.11 even 2